A free-form surface, which is used for the body of various industrial products such as a ship, a car, and an airplane, combines functionality with beauty, and is used for the design engineering of home electrical appliances and many other consumer products that require good form.
Recently, a 3D laser scanner collects high-density point group data speedily and easily, allowing an object shape to be measured accurately. For example, in the field of 3D modeling, a mock-up model manually created by a designer is measured by a 3D laser scanner to create CAD data, such as curved surface data necessary for producing products, based on the point group data and polygon data captured by a computer. This is the so-called the reverse engineering technique for a shape.
In general, a 3D model is represented on a computer using a polygon model or curved surface patches such as NURBS and B-Spline.
In CAD/CAM, curve/curved surface interpolation and approximation methods based on the point group position information, such as B-Spline, NURBS, and subdivision, are known (Non-Patent Document 1, Patent Document 1). In interpolation and approximation, the normal line information may be used, in addition to the position information on points, to increase design flexibility and to increase the approximation accuracy of an offset curve/curved surface.    No-Patent Document 1: Les Piegel, Wayne Tiller “The NURBS Book” P373-P376 Springer-Verlag Berlin Heidenberg 1995 and 1997    Patent Document 1: Japanese Patent Laid-Open Publication No. 2004-192209